Quasiparticle tunneling spectra of the high mercury cuprates: Implications of the-wave two-dimensional van Hove scenario

Quasiparticle tunneling measurements of the high-temperature superconductors (Formula presented) are considered in the context of (Formula presented) symmetry of the superconducting order parameter and a two-dimensional (2D) van Hove singularity (vHs) related to saddle points in the electronic band structure. Normal-metal-insulator-superconductor tunneling spectra taken at 4.2 K with a scanning tunneling microscope on Hg-1212 (Formula presented)-axis epitaxial films, as well as on Hg-1201 and Hg-1223 polycrystalline samples, show distinct gap characteristics which cannot be easily reconciled with the simple (Formula presented)-wave BCS density of states. The data are analyzed with the nodal (Formula presented)-wave gap function (Formula presented) and the 2D tight-binding electronic dispersion (Formula presented) using the quasiparticle tunneling formalism for elastic and specular transmission. The analysis indicates a highly directional and energy-dependent spectral weighting, related to the gap anisotropy and band-structure dependence of the tunneling matrix element (Formula presented) and successfully explains the observed gap spectra. Values for the (Formula presented)-wave gap maximum are determined to be (Formula presented) 50, and 75 meV, respectively, for optimally doped Hg-1201, Hg-1212, and Hg-1223, corresponding to reduced-gap ratios of (Formula presented) 9.5, and 13. These ratios are substantially larger than the BCS weak-coupling limit of 3.54. A comparison with data from other high-(Formula presented) cuprates indicates an overall trend of (Formula presented) rising with (Formula presented) in violation of BCS universality.